A partial differential equation formulation of Vickrey’s bottleneck model, part II: Numerical analysis and computation

The Vickrey model, originally introduced in Vickrey (1969), is one of the most widely used link-based models in the current literature in dynamic traffic assignment (DTA). One popular formulation of this model is an ordinary differential equation (ODE) that is discontinuous with respect to its state variable. As explained in Ban et al. (2011) and Han et al. (2013), such an irregularity induces difficulties in both continuous-time analysis and discrete-time computation. In Han et al. (2013), the authors proposed a reformulation of the Vickrey model as a partial differential equation (PDE) and derived a closed-form solution to the aforementioned ODE. This reformulation enables us to rigorously prove analytical properties of the Vickrey model and related DTA models.